Finite Group Databasebeta

← #28406758

Subgroups — #28406758

Order 14464.

276 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299557C211yesmaximal, characteristic
2#20299542C211yesmaximal, characteristic
3#20299471C214yesmaximal
4C4⋊Q8×D113C211yesmaximal, characteristic
5C2×#14268655C2212yes—
6C2×C4⋊#90673C2212yes—
7#16813677—21no—
8#16813677—21no—
9(C2×#90673)⋊C4—21no—
10(C2×#90673)⋊C4—21no—
11C2×Q8×D113—21no—
12#16813622C411yescharacteristic, complemented
13#16813621—21no—
14#16813621C412yescomplemented
15#16813620—21no—
16C4⋊C4×D113—21no—
17C4⋊C4×D113C2212yes—
18C42×D113C2211yescharacteristic
19C4⋊Q8×C113C411yescharacteristic, complemented
20C22×#90673—22no—
21#14268655—22no—
22#14268655Q814yescomplemented
23C2×#11744753—22no—
24C4⋊#90673—24no—
25C2×Dic226—21no—
26C2×Dic226—22no—
27Q8×D113—44no—
28C2×C4×D113—22no—
29C2×C4×D113D411yescharacteristic
30C2×C4×D113D411yescharacteristic
31C2×C4×D113C2311yescharacteristic
32C4⋊Dic113—21no—
33C4⋊Dic113C2×C412yes—
34#14268626—22no—
35#14268626—22no—
36C4×Dic113C2×C411yescharacteristic
37C4×Dic113D411yescharacteristic
38C4×Dic113D411yescharacteristic
39C2×Q8×C113—21no—
40C4⋊C4×C113—21no—
41C4⋊C4×C113C2×C412yes—
42C42×C113C2×C411yescharacteristic
43C22×D113C2×D411yescharacteristic
44C2×#90673—42no—
45C2×#90673—42no—
46C2×#90673—42no—
47Q8×C113—42no—
48C2×C4×C113—22no—
49C2×C4×C113C22⋊C411yescharacteristic
50C2×C4×C113C22⋊C411yescharacteristic
51C2×C4×C113C22×C411yescharacteristic
52C2×Dic113—22no—
53C2×Dic113C22⋊C411yescharacteristic
54C2×Dic113C22⋊C411yescharacteristic
55C2×Dic113C2×D411yescharacteristic
56C4×D113—22no—
57C4×D113—22no—
58C4×D113—44no—
59C4×D113C2×Q812yes—
60C4×D113#4112yes—
61Dic226—44no—
62Dic226—42no—
63#11744753—24no—
64C22×C113C2×C22⋊C411yescharacteristic
65C2×D113#12411yescharacteristic
66C2×D113C4⋊Q811yescharacteristic
67C2×D113AGL(1,ℤ/8)12yes—
68C2×D113#13712yes—
69#90673—82no—
70C4×C113—21no—
71C4×C113—21no—
72C4×C113—42no—
73C4×C113C4×Q812yes—
74Dic113—21no—
75Dic113—21no—
76Dic113—42no—
77Dic113C22⋊Q812yes—
78C2×C113#39111yescharacteristic
79C2×C113#41811yescharacteristic
80C2×C113#41911yescharacteristic
81D113#48912yes—
82D113#50112yes—
83#1993—1131nomaximal, Sylow
84C113#199311yescharacteristic, complemented, Sylow
85C2×C4⋊Q8—1131no—
86C2×#97—1131no—
87#382—1131no—
88#340—1134no—
89C22×Q8—2261no—
90C22×C8—1132no—
91C4⋊Q8—1132no—
92C4⋊Q8—1131no—
93C4⋊Q8—2261no—
94C4⋊Q8—2261no—
95C4⋊Q8#9067311yescharacteristic, complemented
96C2×C4⋊C4—1132no—
97C2×C4⋊C4—1132no—
98C2×C4⋊C4—2261no—
99C2×C42—1131no—
100#97—2261no—
101#97—2261no—
102#95—2261no—
103#95—2261no—
104C2×Q8—21no—
105C2×Q8—4524no—
106C2×Q8—2262no—
107C2×Q8—2261no—
108C22×C4—1131no—
109C22×C4—1131no—
110C22×C4—1131no—
111C22×C4—2262no—
112C22×C4—2262no—
113C2×C8—1134no—
114C2×C8—2262no—
115C2×C8—2262no—
116C4⋊C4—21no—
117C4⋊C4—1132no—
118C4⋊C4—2262no—
119C4⋊C4—2262no—
120C4⋊C4—2264no—
121C4⋊C4—2261no—
122C4⋊C4C2×#9067312yes—
123C42—1131no—
124C42—1131no—
125C42—1131no—
126C42C2×#9067311yescharacteristic
127C23—1131no—
128Q8—42no—
129Q8—4522no—
130Q8—4524no—
131C2×C4—22no—
132C2×C4—1131no—
133C2×C4—1132no—
134C2×C4—1132no—
135C2×C4—1131no—
136C2×C4—1131no—
137C2×C4—4524no—
138C2×C4—4522no—
139C2×C4—4522no—
140C2×C4—4522no—
141C2×C4—2262no—
142C2×C4—2262no—
143C2×C4—2262no—
144C2×C4C22⋊#9067311yescharacteristic
145C2×C4C22⋊#9067311yescharacteristic
146C2×C4C22×#9067311yescharacteristic
147C8—2264no—
148C22—1131no—
149C22—1131no—
150C22—1132no—
151C22—1132no—
152C22C2×C22⋊#9067311yescharacteristic
153C4—21no—
154C4—21no—
155C4—42no—
156C4—1132no—
157C4—9042no—
158C4—4522no—
159C4—2261no—
160C4—2261no—
161C4Q8×#9067312yes—
162C2—1132no—
163C2—1132no—
164C2(C2×#90673)⋊Q811yescharacteristic
165C2#2029959011yescharacteristic
166C2#2029959111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC4⋊Q8×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC22×D113C2×D4
cosocleC2×C4×D113C23
hypercenterC4⋊Q8#90673
hypocenterC113#1993
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
12. #16813622C4semidirect
14. #16813621C4semidirect
19. C4⋊Q8×C113C4semidirect
22. #14268655Q8semidirect
84. C113#1993semidirect
95. C4⋊Q8#90673semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202995572
#202995422
#202994712
C4⋊Q8×D1132
#1993113